Dog's in river for a period (6)
I believe the answer is:
decade
'a period' is the definition.
(decade is a kind of period)
'dog's in river' is the wordplay.
'dog' becomes 'cad' ('cad' can be a synonym of 'dog'**).
'in' is an insertion indicator.
'river' becomes 'dee' (River Dee).
'cad' going into 'dee' is 'DECADE'.
'for' is the link.
(Other definitions for decade that I've seen before include "number of years" , "Period of ten years" , "Ten year period" , "The noughties, say" , "Series of 10 years" .)